(12z-15)(12z-21)=0

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Solution for (12z-15)(12z-21)=0 equation: 


Simplifying
(12z + -15)(12z + -21) = 0

Reorder the terms:
(-15 + 12z)(12z + -21) = 0

Reorder the terms:
(-15 + 12z)(-21 + 12z) = 0

Multiply (-15 + 12z) * (-21 + 12z)
(-15(-21 + 12z) + 12z * (-21 + 12z)) = 0
((-21 * -15 + 12z * -15) + 12z * (-21 + 12z)) = 0
((315 + -180z) + 12z * (-21 + 12z)) = 0
(315 + -180z + (-21 * 12z + 12z * 12z)) = 0
(315 + -180z + (-252z + 144z2)) = 0

Combine like terms: -180z + -252z = -432z
(315 + -432z + 144z2) = 0

Solving
315 + -432z + 144z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '9'.
9(35 + -48z + 16z2) = 0

Factor a trinomial.
9((5 + -4z)(7 + -4z)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(5 + -4z)' equal to zero and attempt to solve:

Simplifying
5 + -4z = 0

Solving
5 + -4z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4z = 0 + -5
-4z = 0 + -5

Combine like terms: 0 + -5 = -5
-4z = -5

Divide each side by '-4'.
z = 1.25

Simplifying
z = 1.25

Subproblem 2
Set the factor '(7 + -4z)' equal to zero and attempt to solve:

Simplifying
7 + -4z = 0

Solving
7 + -4z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -4z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4z = 0 + -7
-4z = 0 + -7

Combine like terms: 0 + -7 = -7
-4z = -7

Divide each side by '-4'.
z = 1.75

Simplifying
z = 1.75
Solution
z = {1.25, 1.75}

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